First-order logic—also called predicate logic, predicate calculus, quantificational logic—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables, so that rather than propositions such as "Socrates is a man", one can have expressions in the form "there exists x such that x is Socrates and x is a man", where "there exists" is a quantifier, while x is a variable. This distinguishes it from propositional logic, which does not use quantifiers or relations; in this sense, propositional logic is the foundation of first-order logic.
Linguistics is the scientific study of human language. Someone who engages in this study is called a linguist. See also the Outline of linguistics, the List of phonetics topics, the List of linguists, and the List of cognitive science topics. Articles related to linguistics include:
Categorial grammar is a family of formalisms in natural language syntax that share the central assumption that syntactic constituents combine as functions and arguments. Categorial grammar posits a close relationship between the syntax and semantic composition, since it typically treats syntactic categories as corresponding to semantic types. Categorial grammars were developed in the 1930s by Kazimierz Ajdukiewicz and in the 1950s by Yehoshua Bar-Hillel and Joachim Lambek. It saw a surge of interest in the 1970s following the work of Richard Montague, whose Montague grammar assumed a similar view of syntax. It continues to be a major paradigm, particularly within formal semantics.
The theory of descriptions is the philosopher Bertrand Russell's most significant contribution to the philosophy of language. It is also known as Russell's theory of descriptions. In short, Russell argued that the syntactic form of descriptions is misleading, as it does not correlate their logical and/or semantic architecture. While descriptions may seem like fairly uncontroversial phrases, Russell argued that providing a satisfactory analysis of the linguistic and logical properties of a description is vital to clarity in important philosophical debates, particularly in semantic arguments, epistemology and metaphysical elements.
In linguistics, anaphora is the use of an expression whose interpretation depends upon another expression in context. In a narrower sense, anaphora is the use of an expression that depends specifically upon an antecedent expression and thus is contrasted with cataphora, which is the use of an expression that depends upon a postcedent expression. The anaphoric (referring) term is called an anaphor. For example, in the sentence Sally arrived, but nobody saw her, the pronoun her is an anaphor, referring back to the antecedent Sally. In the sentence Before her arrival, nobody saw Sally, the pronoun her refers forward to the postcedent Sally, so her is now a cataphor. Usually, an anaphoric expression is a pro-form or some other kind of deictic expression. Both anaphora and cataphora are species of endophora, referring to something mentioned elsewhere in a dialog or text.
In linguistics, coreference, sometimes written co-reference, occurs when two or more expressions refer to the same person or thing; they have the same referent. For example, in Bill said Alice would arrive soon, and she did, the words Alice and she refer to the same person.
In formal linguistics, discourse representation theory (DRT) is a framework for exploring meaning under a formal semantics approach. One of the main differences between DRT-style approaches and traditional Montagovian approaches is that DRT includes a level of abstract mental representations within its formalism, which gives it an intrinsic ability to handle meaning across sentence boundaries. DRT was created by Hans Kamp in 1981. A very similar theory was developed independently by Irene Heim in 1982, under the name of File Change Semantics (FCS). Discourse representation theories have been used to implement semantic parsers and natural language understanding systems.
Andrea Bonomi is an Italian philosopher and logician, who studied with Enzo Paci.
Computational semantics is the study of how to automate the process of constructing and reasoning with meaning representations of natural language expressions. It consequently plays an important role in natural-language processing and computational linguistics.
Combinatory categorial grammar (CCG) is an efficiently parsable, yet linguistically expressive grammar formalism. It has a transparent interface between surface syntax and underlying semantic representation, including predicate–argument structure, quantification and information structure. The formalism generates constituency-based structures and is therefore a type of phrase structure grammar.
Quantificational variability effect (QVE) is the intuitive equivalence of certain sentences with quantificational adverbs (Q-adverbs) and sentences without these, but with quantificational determiner phrases (DP) in argument position instead.
Johan Anthony Willem "Hans" Kamp is a Dutch philosopher and linguist, responsible for introducing discourse representation theory (DRT) in 1981.
A bound variable pronoun is a pronoun that has a quantified determiner phrase (DP) – such as every, some, or who – as its antecedent.
Dynamic semantics is a framework in logic and natural language semantics that treats the meaning of a sentence as its potential to update a context. In static semantics, knowing the meaning of a sentence amounts to knowing when it is true; in dynamic semantics, knowing the meaning of a sentence means knowing "the change it brings about in the information state of anyone who accepts the news conveyed by it." In dynamic semantics, sentences are mapped to functions called context change potentials, which take an input context and return an output context. Dynamic semantics was originally developed by Irene Heim and Hans Kamp in 1981 to model anaphora, but has since been applied widely to phenomena including presupposition, plurals, questions, discourse relations, and modality.
This is an index of Wikipedia articles in philosophy of language
Formal semantics is the study of grammatical meaning in natural languages using formal tools from logic, mathematics and theoretical computer science. It is an interdisciplinary field, sometimes regarded as a subfield of both linguistics and philosophy of language. It provides accounts of what linguistic expressions mean and how their meanings are composed from the meanings of their parts. The enterprise of formal semantics can be thought of as that of reverse-engineering the semantic components of natural languages' grammars.
Craige Roberts is an American linguist, known for her work on pragmatics and formal semantics.
In formal semantics, the scope of a semantic operator is the semantic object to which it applies. For instance, in the sentence "Paulina doesn't drink beer but she does drink wine," the proposition that Paulina drinks beer occurs within the scope of negation, but the proposition that Paulina drinks wine does not. Scope can be thought of as the semantic order of operations.
In formal semantics and pragmatics, modal subordination is the phenomenon whereby a modal expression is interpreted relative to another modal expression to which it is not syntactically subordinate. For instance, the following example does not assert that the birds will in fact be hungry, but rather that hungry birds would be a consequence of Joan forgetting to fill the birdfeeder. This interpretation was unexpected in early theories of the syntax-semantics interface since the content concerning the birds' hunger occurs in a separate sentence from the if-clause.
- If Joan forgets to fill the birdfeeder, she will feel very bad. The birds will get hungry.
In formal semantics, existential closure is an operation which introduces existential quantification. It was first posited by Irene Heim in her 1982 dissertation, as part of her analysis of indefinites. In her formulation, existential closure is a form of unselective binding which binds any number of variables of any semantic type. In alternative semantics and related frameworks, the term is often applied to a closely related operation which existentially quantifies over a set of propositional alternatives.
